Analytic Sinusoidal Steady-State Electromagnetic Field Expressions for the Ideal Veselago Lens

Abstract

Analytic expressions for the sinusoidal steady-state electromagnetic field associated with an ideal Veselago lens illuminated by either a line-source (2D case) or an electric dipole point-source (3D case) are obtained based on power flow considerations and the imposition of appropriate boundary conditions. The fields are written in terms of the standard free-space Green’s function except that both incoming and outgoing waves are utilized. Expressions for the Poynting vector are also provided. Some components of the field suffer a complex-conjugate discontinuity across two power-transfer singularity planes, one within the lens and one through the external focus point, so named because all the power generated by the point-source transfers through a singular point on each plane. The internal power-transfer singular point and the illuminating point-source are equidistant from the first lens boundary, whereas the external singular point, i.e., the focus point, and the internal singular point are equidistant from the second lens boundary. These singularities represent different physical properties than the traditional source or sink singularities. The new interpretation based on the concise analytic field expressions clears up the physically objectionable interpretation of these singularities as representing new sources of energy: no new sources of energy exist in our representations.

Keywords

• Double-negative
• green’s function
• metamaterials
• Veselago lens